Systems of Nonlinear Differential Equations and Ecology : Basics, Concepts, Methods

The study of systems of nonlinear differential equations will be very useful to analyze the possible past or future outcomes with the help of present information in any natural dynamical systems. The present book studies some autonomous nonlinear systems of ordinary differential equations. It focuses on their applications to population dynamics problems in mathematical ecology. In particular, the following aspects are the main objectives of the present work: I) The stability of the equilibrium points. II) The behavior of solution around equilibrium points. The first chapter presents some standard basic concepts, definitions, notations, theorems and methods. The second chapter is devoted to the study of Kolmogrov models of population dynamics; Rosenweig-Mac Artur model; including competition and coexistence factors for mutual benefit of two species. The third and fourth chapters analyze the extended Lotka-Volterra predator-prey models including intraspecies factors. The behavior of solution around these equilibrium points are studied in detail.